Assume that the cyclic \(L_\infty \)  algebra
\((\mathcal {H}_l,\omega _l,L^{(0,0)}=\sum _{n=0}^\infty L^{(0,0)}_{n+1})\) 
without picture number, which is straightforwardly constructed similar to that
of the bosonic string field theory [1]}, [2]}, [3]},
is knownThis is actually a cyclic \(L_\infty \)  algebra \((\mathcal {H},\omega _s,L^{(0,0)})\) 
closed in the small Hilbert space..
We define a generating functional
\(L^{(0,0)}(s,\bar{s})\ =\ Q + \sum _{m,\bar{m},r,\bar{r}}s^m\bar{s}^{\bar{m}}L^{(0,0)}_{m+r+1,\bar{m}+\bar{r}+1}\mid ^{(2r,2\bar{r})}\ \equiv \ Q + L^B(s,\bar{s})\,,\) 
